Imam Hussein went to Mecca and stayed there for four months. He visited different groups and wrote a lot of letters to Kufa, Basra, and to individuals. He went on a pilgrimage to Kaba and he visited the tombs of diseased predecessors; he went to the Aboutalib Cemetery and visited the graves of his great grandfather, Aboutaleb (A.S), and his great grandmother, Khadijeh (SA). He said his prayers right there.
When he learnt about the plots of his enemies, who were trying to kill him, he decided to leave Mecca as a sign of his respect to Kaba. This is the most beautiful respect one could have for the House of God. Imam Hussein did not want to do what Abdullah bin Zubayr did; he took refuge in Kaba, and doing this, he actually disrespected the holy place.
Hussein bin Ali (A.S) treated Abdullah bin Zubayr respectfully and told the people, “Ibn Zubayr wants me to take refuge in the holy shrine, but I would rather be far from the House of God in the time of death. I would rather die next to the Euphrates, than in Kaba.”
It is also said that Abdullah bin Zubayr told Imam Hussein (A.S) to stay in Mecca and to take refuge in Kaba. Imam Hussein answered, “This is not a right thing to do. I do not think that I should do that. I would rather get killed in the desert than in Mecca.”
With all the respect Imam Hussein accorded to Kaba, he left it, tears in his eyes.
He went to Karbala, because he did not want anyone or anything to disrespect Kaba, the House of God.a
source : tebyan
